A042758 Numerators of continued fraction convergents to sqrt(910).

30, 181, 10890, 65521, 3942150, 23718421, 1427047410, 8586002881, 516587220270, 3108109324501, 187003146690330, 1125126989466481, 67694622514679190, 407292862077541621, 24505266347167176450, 147438890945080600321, 8870838723052003195710

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0,362,0,-1).

Crossrefs

Cf. A042759.

Programs

Magma

I:=[30, 181, 10890, 65521]; [n le 4 select I[n] else 362*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 04 2013

Mathematica

Numerator[Convergents[Sqrt[910], 30]] (* or *) CoefficientList[Series[(30 + 181 x + 30 x^2 - x^3)/(1 - 362 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 04 2013 *)

Formula

G.f.: (30 +181*x +30*x^2 -x^3)/(1 -362*x^2 +x^4). - Vincenzo Librandi, Dec 04 2013

a(n) = 362*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 04 2013

Extensions

More terms from Vincenzo Librandi, Dec 04 2013